Optical microscopy is among the oldest applications of optical science and remains one of the most widely used optical technologies. In spite of impressive results obtained by fluorescent microscopy in exceeding the classical diffraction limit, non-fluorescent transmission/reflection microscopy remains an important field of modern research. However, using traditional illumination schemes, resolution is limited to ˜K1λ/NA where λ is the source wavelength and NA is the numerical aperture (sine of the half-acceptance angle) of the imaging objective lens. The “constant” K1 depends on both the details of the image and on the illumination scheme. For example, K1 can be between 0.25 and 1. Hence, traditional approaches to improve resolution are either to use shorter wavelengths and/or to use larger numerical-aperture lenses. For biological samples, however, the wavelength is constrained to the visible spectral range because ultraviolet photons can damage samples. In many practical cases, even for inorganic samples, the wavelength is limited to the deep ultraviolet (for example 193 nm) since transmissive optical materials become difficult at shorter wavelengths (fused quartz has a cutoff at ˜185 nm). Furthermore, a disadvantage of using a high-NA lens is the resulting short depth-of-field (an essential feature of achieving high resolution in a single image; typically the depth-of-field scales as K2λ/NA2 where K2 is a second “constant” of order unity). The depth-of-field decreases rapidly as the NA is increased to increase the resolution. In addition, the field of view (the area over which the resolution is achieved) and the working distance (the distance from the final lens surface to the object plane) are reduced for higher-NA optical systems. These latter two issues can be surmounted by more complex objective lenses, with an increase in the cost of manufacturing. These tradeoffs are well known and are discussed in many microscopy overviews.
Synthetic aperture approaches, such as, for example, imaging interferometric microscopy (IIM), extend the collected spatial frequencies to improve the image. IIM, with both illumination and collection in a transmission medium (usually air), uses a low-NA objective and yet provides a resolution approximately a factor of two better than that available even with a high-NA objective using conventional coherent or incoherent illumination. A major advantage is that the depth-of-field, field-of-view and working distance associated with the low-NA system are retained, but the final composite image has a resolution at the linear system limit imposed by the transmission medium (≳λ/4n where λ is the wavelength in free space and n is the index of refraction of the transmission medium), and significantly better than that accessible with even a high NA lens using conventional (coherent or incoherent) illumination approaches.
An exemplary IIM with two offset partial images, one each in orthogonal spatial directions can result in an increased resolution by three times using about 0.4-NA objective and 633-nm He—Ne laser. Furthermore, IIM requires building an interferometric system around the objective lens which is an issue for wide-spread adoption of this approach, and in particular towards its adoption to the existing microscopes. In the prior art, this interferometer required additional optics to relay the pupil plane of the collection objective to convenient location; this is straightforward but required significant additional optics. Hence, there is a need for a new approach that does not require a large change to the imaging optical system that comprises the objective lens and subsequent optical components.
The prior art imaging interferometric microscopy was able to image maximum spatial frequency of 2π/λ e.g. to the linear system's limit of the air (transmission medium between the object and the lens). The ultimate linear system limit is 2πn/λ, which reflects the use of an immersion medium of refractive index n. Even though materials with refractive indices of up to about 5 are known at some optical wavelengths, the highest numerical aperture available for the immersion microscopy is about 1.4, limited by the refractive index of the glass used to make the lens, by the refractive indices available for the index matching fluids, and the well known difficulties of making aberration corrected optics of high NA. Hence, there is a need for a new approach that can achieve this linear system limit without requiring index-matching fluids or high NA lenses.
As is well-known, using off-axis illumination provides enhanced resolution over that available with either of the standard illumination schemes discussed above, but there is some distortion of the image associated with the resultant non-constant transfer function for different regions of frequency space. This non-uniform frequency-space coverage can be addressed with appropriate pupil plane filters and by combining partial images corresponding to different parts of frequency space, as has been previously demonstrated in the case of imaging interferometric lithography